I guess most of the problems are relatively small, but for Advent of Code¹, the "competitive" people are finishing most of their solutions in a minute or two.

1. http://adventofcode.com/

How will you look it up when necessary during a programming contest (like the IOI/ICPC mentioned in the book)? It's usually not allowed by the contest rules to look up an entire book's worth.

And if your teams algo and data structure knowledge isn't at the level where you know about these solutions or their applicability?

I have a checklist of possible interview topics and I think I might an esoteric data structure part to it (knowledge not code) and some implementation choice questions - given this situation and data, with these queries what would your data structures look like.

Maybe also a few quotations on the last paper they've read in CS or related topic.

Why test for anything in an interview? Why not assume anyone can learn everything on the job?